Problem: One day mum asked Petya to sort his toys and get rid of some of them. Petya found a whole box of toy spiders. They were quite dear to him and the boy didn't want to throw them away. Petya conjured a cunning plan: he will glue all the spiders together and attach them to the ceiling. Besides, Petya knows that the lower the spiders will hang, the more mum is going to like it and then she won't throw his favourite toys away. Help Petya carry out the plan.

A spider consists of k beads tied together by k - 1 threads. Each thread connects two different beads, at that any pair of beads that make up a spider is either directly connected by a thread, or is connected via some chain of threads and beads.

Petya may glue spiders together directly gluing their beads. The length of each thread equals 1. The sizes of the beads can be neglected. That's why we can consider that gluing spiders happens by identifying some of the beads (see the picture). Besides, the construction resulting from the gluing process should also represent a spider, that is, it should have the given features. 

After Petya glues all spiders together, he measures the length of the resulting toy. The distance between a pair of beads is identified as the total length of the threads that connect these two beads. The length of the resulting construction is the largest distance between all pairs of beads. Petya wants to make the spider whose length is as much as possible.

<image> <image>

The picture two shows two spiders from the second sample. We can glue to the bead number 2 of the first spider the bead number 1 of the second spider. The threads in the spiders that form the sequence of threads of maximum lengths are highlighted on the picture.

Input

The first input file line contains one integer n (1 ≤ n ≤ 100) — the number of spiders. Next n lines contain the descriptions of each spider: integer ni (2 ≤ ni ≤ 100) — the number of beads, then ni - 1 pairs of numbers denoting the numbers of the beads connected by threads. The beads that make up each spider are numbered from 1 to ni.

Output

Print a single number — the length of the required construction.

Examples

Input

1
3 1 2 2 3


Output

2


Input

2
3 1 2 1 3
4 1 2 2 3 2 4


Output

4


Input

2
5 1 2 2 3 3 4 3 5
7 3 4 1 2 2 4 4 6 2 7 6 5


Output

7

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.math.*;

import static java.lang.Math.*;

public class Main implements Runnable {

    StreamTokenizer in;
    BufferedReader reader;
    PrintWriter out;
    StringTokenizer tok;
    Scanner sc;
    boolean timus =true;// System.getProperty("ONLINE_JUDGE")!=null;
    boolean codeforces = false;
    final double eps = 1e-9;
    
    public static void main(String[] args) throws Exception {
        new Thread(new Main()).start();
    }
    
    @Override
    public void run() {
        try {
            if (codeforces) {
                sc = new Scanner(System.in);
                reader = new BufferedReader(new InputStreamReader(System.in));
                in = new StreamTokenizer(reader);
                out= new PrintWriter (new OutputStreamWriter(System.out));
                tok = new StringTokenizer("");
                solve();
                out.flush();
            } else
                if (timus) {
                    sc = new Scanner("input.txt");
                    reader = new BufferedReader(new FileReader("input.txt"));
                    in = new StreamTokenizer(reader);
                    out= new PrintWriter (new FileWriter("output.txt"));
                    tok = new StringTokenizer("");
                    solve();
                    out.flush();
                    out.close();
                } else
                    if (!timus) {
                long begMem = Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory();
                long t1 = System.currentTimeMillis();
                reader = new BufferedReader(new InputStreamReader(System.in));
                in = new StreamTokenizer(reader);
                sc = new Scanner(System.in);
                out= new PrintWriter (new OutputStreamWriter(System.out));
                tok = new StringTokenizer("");
                solve();
                long endMem = Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory();
                out.flush();
                long t2 = System.currentTimeMillis();
                System.out.println("Time:"+(t2-t1));
                System.out.println("Memory:"+(endMem-begMem));
                System.out.println("Total memory: " + (Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory()));
            }
        }
        catch (Exception ex) {
            System.out.println("fail");
            System.exit(1);
        }
    }
    
    public class Chess {
        String coord;
        
        public Chess(String s){
            this.coord=s;
        }
        
        public int toInteger(char s) {
            if (s=='a'||s=='A') return 1;
            else if (s=='b'||s=='B') return 2;
            else if (s=='c'||s=='C') return 3;
            else if (s=='d'||s=='D') return 4;
            else if (s=='e'||s=='E') return 5;
            else if (s=='f'||s=='F') return 6;
            else if (s=='g'||s=='G') return 7;
            else if (s=='h'||s=='H') return 8;
            else return -1;
        }
        
        public String toString(int s) {
            if (s==1) return "a";
            else if (s==2) return "b";
            else if (s==3) return "c";
            else if (s==4) return "d";
            else if (s==5) return "e";
            else if (s==6) return "f";
            else if (s==7) return "g";
            else if (s==8) return "h";
            else return "0";
        }
        
        public pair getPair() {
            String j="";
            j+=coord.charAt(1);
            pair p = new pair(toInteger(coord.charAt(0)),Integer.parseInt(j));
            if (p.x!=-1)
            return p; else
                return new pair(0,0);
        }
        
        public String returnPair(pair p) {
            return toString(p.x)+p.y;
        }
    }
    
    public int nextInt() throws Exception {
        in.nextToken();
        return (int) in.nval;
    }
    
    public String next() throws Exception {
        in.nextToken();
        return in.sval;
    }
    
    public String nextLine() throws Exception {
        return reader.readLine();
    }
    
    public String nextString() throws Exception {
        while (!tok.hasMoreTokens())
            tok = new StringTokenizer(reader.readLine());
        return tok.nextToken();
    }
    
    public long nextLong() throws Exception {
        return Long.parseLong(nextString());
    }
    
    public double nextDouble() throws Exception {
        in.nextToken();
        return in.nval;
    }
    
    public class pair {
        int x;
        int y;
        
        public pair(int x, int y) {
            this.x=x;
            this.y=y;
        }
    }
    
    public int gcd(int a, int b) {
        if (a== 0||b==0) return 1;
        if (a<b) {
                int c=b;
                b=a;
                a=c;
        }
        while (a%b!=0) {
                a =a%b;
                if (a<b) {
                        int c=b;
                        b=a;
                        a=c;
                }
        }
        return b;
    }
    
     public int pow(int a, int n) {
         if (n==0) return 1;
         int k=n, b=1, c=a;
         while (k!=0) {
                 if (k%2==0) {
                         k/=2;
                         c*=c;
                 } else {
                         k--;
                         b*=c;
                 }
         }
         return b;
     }
    
    public int lcm(int a, int b) {
        return a*b/gcd(a,b);
    }
    
    public class pairs implements Comparable<pairs> {
        int x;
        int y;
        
        public pairs(int x, int y) {
            this.x=x;
            this.y=y;
        }

        @Override
        public int compareTo(pairs obj) {
            if (this.x<((pairs)obj).x) return 1;
            else if (this.x==(obj).x&&this.y<(obj).y) return 1;
            else if (this.x==(obj).x&&this.y==(obj).y)return 0; else
                return -1;
        }   
    }
    
    public class Graf {
        
        int [][] a;
        int [] colors;
        ArrayList <String> points = new ArrayList<String>();
        LinkedList <Integer> queue = new LinkedList <Integer>();
        boolean [] used;
        boolean cycle;
        int numberOfCycle;
        
        public Graf(int [][]a,String s[]) {
            this.a=new int [s.length][s.length];
            this.a=a;
            this.colors=new int [s.length];
            this.used=new boolean[s.length];
            for (int i=0; i<s.length;i++) {
                this.colors[i]=0;
                this.points.add(s[i]);
            }
            Arrays.fill(this.used, false);
        }
        
        public void bfs(int i) {
            this.queue.add(i);
            while (!this.queue.isEmpty())
            {
                i = this.queue.pop();
                out.print(points.get(i)+" ");
                this.used[i]=true;
                for (int j=0; j<this.points.size();j++) {
                    if (this.a[i][j]==1&&!this.queue.contains(j)&&!this.used[j]) {
                        this.a[i][j]=0;
                        this.a[j][i]=0;
                        this.queue.addLast(j);
                    }
                }
            }
        }
        
        public void dfs(int i) {
            this.colors[i]=1;
            out.print(points.get(i)+" ");
            for (int j=0; j<this.colors.length;j++) {
                if (this.a[i][j]==1&&this.colors[j]==0) {
                    this.colors[j]=1;
                    this.a[i][j]=0;
                    this.a[j][i]=0;
                    dfs(j);
                } else if (this.a[i][j]==1&&this.colors[j]==1) {
                    this.cycle=true;
                    this.numberOfCycle++;
                }
            }
            this.colors[i]=2;
        }   
    }
    
    public class Time {
        
        int h;
        int min;
        int sec;
        
        public Time(String s) {
            String [] st = s.split(":");
            this.h =Integer.parseInt(st[0]);
            this.min =Integer.parseInt(st[1]);
            this.sec =(st[2]!=null)? Integer.parseInt(st[2]):0;
        }
        
        public String toString(int a) {
            String h = Integer.toString(this.h);
            String min = Integer.toString(this.min);
            String sec = Integer.toString(this.sec);
            if (h.length()==1) {
                h='0'+h;
            }
            if (min.length()==1) {
                min='0'+min;
            }
            if (sec.length()==1) {
                sec='0'+sec;
            }
            if (a==5) {
                return h+":"+min;
            } else {
                return h+":"+min+":"+sec;
            }
        }
        
        public void to12HoursFormat () {
            h%=12;
        }
        
        public void add (int  h,int min,int s) {
            this.sec+=s;
            if (this.sec>=60) {
                this.min++;
                this.sec%=60;
            }
            this.min+=min;
            if (this.min>=60) {
                this.h++;
                this.min%=60;
            }
            this.h+=h;
            if (this.h>=24) {
                this.h%=24;
            }
        }
    }
    
    public int[] findPrimes(int x) {
        boolean[] erat = new boolean[x-1];
        List<Integer> t = new ArrayList<Integer>();
        int l=0, j=0;
        for (int i=2;i<x; i++) {
                if (erat[i-2]) continue;
                t.add(i);
                l++;
                j=i*2;
                while (j<x) {
                        erat[j-2]=true;
                        j+=i;
                }
        }
        int[] primes = new int[l];
        Iterator<Integer> iterator = t.iterator();
        for (int i = 0; iterator.hasNext(); i++) {
                primes[i]=iterator.next().intValue();
        }
        return primes;
    }
    
    public double dist(pair a,pair b) {
        return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
    }
    
    int max_val=Integer.MIN_VALUE;
    
    public void dfs (int current, int prev, int max,int a[][]) {
        int n = a[0].length;
        for (int i=0; i<n;i++) {
            if (a[current][i]==1&&prev!=i) {
                dfs(i,current,max+1,a);
            }
        }
        max_val = max(max_val,max);
    }
    
    public void solve() throws Exception {
        int n = nextInt();
        int ans=0;
        for (int i=0; i<n;i++) {
            int k = nextInt();
            int [] b= new int [k];
            int a[][] = new int [k][k];
            for (int j=0; j<k-1;j++) {
                int x = nextInt();
                int y = nextInt();
                a[x-1][y-1]=1;
                a[y-1][x-1]=1;
                b[x-1]++;
                b[y-1]++;
            }
            ArrayList <Integer> al = new ArrayList <Integer>();
            for (int j=0;j<k;j++) {
                if (b[j]==1) {
                    al.add(j);
                }
            }
            for (int q:al) {
                dfs(q,-1,0,a);
            }
            ans+=max_val;
            max_val=Integer.MIN_VALUE;
        }
        out.println(ans);
    }
}